Learning Math the “New” Way

Learning Math the “New” Way Building a Strong Foundation of Number Sense Laurie Culpepper Kim Brown Joan Englade

Place Value – Third Grade

Place Value – Fourth Grade

Place Value – Fifth Grade

Renaming Numbers • It is important that your child see that numbers can be written different ways. • For example – 356 = 3 hundreds + 5 tens = 6 ones OR 35 tens + 6 ones OR 3 hundreds + 56 ones • 4,586 = 4 thousands + 5 hundreds + 8 tens + 6 ones OR 45 hundreds + 8 tens + 6 ones OR 458 tens + 6 ones OR 45 hundreds + 86 ones • Place value is so important when your child looks at a number – we want them to see the value of a number, not just digits.

Ways to Write Numbers • Standard Form: 405,612 • Word Form: Four hundred five thousand, six hundred twelve • Expanded Form: (shows the value of each digit) 400,000 + 5,000 + 600 + 10 + 2

Difficulties with Standard/Written Form • Standard to Written Form • Students have difficulties with zeros in the number • Reinforce to your child that commas say the period’s name • We NEVER say the word “and” except at the decimal point • Example: 78,030 – seventy-eight thousand, thirty 843,900,401 – eight hundred forty-three million, nine hundred thousand, four hundred one 23,000,154,802 – twenty-three billion, one hundred fifty-four thousand, eight hundred two (notice there is nothing in the millions place, so we don’t write millions) 45.34 – forty-five and thirty-four hundredths

Difficulties with Standard/Written Form • Written to Standard Form • Biggest mistake that kids make is not writing 3 digits in each period or forgetting to write zeros to represent a period (those dreaded zeros) • Example: five hundred sixteen million, forty-two thousand, eight hundred fourteen – 516,042,814 not 516,42,814 six hundred five billion, thirty-two thousand, one hundred twelve – 605,000,032,112 not 605,32,112

Rounding • 3rd grade rounds to the nearest ten and hundred • 4th grade rounds to the nearest ten, hundred and thousand • 5th grade is expected to round to any place value including tenths and hundredths. • Strategies that are used include “rounding hill” and “fork in the road”

Rounding Hill

Rounding/Fork in the Road

Addition (Expanded Form) • One strategy that is taught is to add using expanded form. • WHY? Because we want kids to have good number sense and NOT see a number like 437 as a 4, a 3 and a 7 • Examples:

Addition (Unmarked Number Line) • 163 + 152 Added 152 +100 +30 +10 +5 +5 +2 163 165 200 170 210 215 315 answer

Subtraction (Subtracting in Parts) • Subtracting in Parts asks students to subtract a number in parts using expanded form • We don’t want kids to just use a rule, but to understand what is happening when we subtract • Examples:

Subtraction (Unmarked Number Line) • 473 - 327 Added 146 Answer +100 +43 +3 327 330 373 473 Start End

Subtraction (Adding Up) • Adding up has the student starting at the smaller number and adding on amounts until they get to the larger number. • Examples:

Subtraction (Subtracting Back) • Subtracting Back is opposite of Adding Up • Student starts at the larger number and subtracts back until they get to the smaller number. • Examples:

Subtraction (Regrouping) • Students have a very difficult time understanding regrouping or “borrowing”, especially over zeros. • Have your child write it out in expanded form so they can see why 0’s turn to 9’s, etc. • Examples:

Multiplication (Arrays) • After learning multiplication facts in 3rd grade, 2 digit by 1 digit multiplication is the next concept taught. It is first represented by arrays with place value blocks.

Multiplication (Arrays) 10x10 = 100 10x10 = 100 10x10 = 100 10x10 = 100

Multiplication (Partial Products) • Partial Products has the student break the numbers into expanded form and multiply each part of the problem together.

Multiplication (Clustering) • Clustering has kids looks at patterns and use that knowledge to help them solve the problem. • We do it in a story context to help us “see” what part of the problem we have done.

Division (Backwards Clustering) • When talking about division, we talk about making equal groups and do it in clusters. • Again, we use a story context to help us “see” what part of the problem we have solved.

Division (Making Equal Groups) • This looks closest to the traditional way that we all learned growing up. The only difference is that the students see how many equal groups we can make and subtract to see what we have left. We never “bring down” any numbers. • Helps them to see what is really happening when you are dividing. Kids have trouble consistently using the “rule” of divide, multiply, subtract, compare, bring down. This avoids the rules and has them understand what division is: a PROCESS and NOT a RULE.

Division (continued)

Why are we doing this? • To prevent this:

Why are we doing this? • And this:

Why are we doing this? • Or this:

Why are we doing this? • We want them to do this: • What is ¼ of 200?

Why are we doing this? • We want them to do this: • What is ¾ + 9/6?

How does this relate to other areas in math? • Elapsed Time: I went to a movie at 3:15 and was over at 6:05. How long was the movie? Add on to 3:15 until they get to 6:05 (Adding Up Strategy). • Measurement: I have 2 ft 3 inches of yarn. How much more yarn do I need to make 4 feet of yarn? Start at 4 feet and take away 2 feet and then 3 more inches. (Subtracting in Parts Strategy) • Algebra: What is (3x + 5)(x + 4)? Use the box method and use partial products to get 3x2 +12x + 5x + 20 or 3x2 + 17x + 20 (Get ready folks – it is coming in MS.)

Thanks for coming tonight! Let us know if we can help you in anyway. We are here to help you. Laurie Culpepper (3rd) – culpeppl@friscoisd.org Kim Brown (4th) – brownk@friscoisd.org Joan Englade (5th) – engladej@friscoisd.org

Learning Math the “New” Way